The little latch on the plug will not fully latch on. Is this normal?
No that's not normal.
How much force is needed to plug it in?
Try a little more,make sure the motherboard is on a flat surface.If this doesn't work get in contact with the seller(s) and discuss replacement of either the psu or motherboard.You could see if the psu will connect with another motherboard,maybe from a friends pc ... if it works fine there is it the motherboard that needs to be replaced.